
import pandas as pd
import numpy as np

import matplotlib.pyplot as plt
import matplotlib.dates as mdates

from scipy import signal
from statsmodels.tsa.stattools import grangercausalitytests
from statsmodels.tsa.ar_model import AutoReg
from statsmodels.tsa.arima.model import ARIMA

from sklearn.metrics import r2_score, median_absolute_error, mean_absolute_error
from sklearn.metrics import median_absolute_error, mean_squared_error, mean_squared_log_error

from pathlib import Path

import os, sys
sys.path.insert(0, os.path.abspath('../src'))

from ts import *
from utils import *


data_path = "../data"


DataDownloader(data_path).download_all_csv()


covidpro_df, dpc_regioni_df, _, _, _ = load_data(data_path)


province = "Firenze"
compart = "New_cases"
date = 'Date'


tmp_df = covidpro_df[covidpro_df.Province == province]


visualize_ts(tmp_df, date, compart, province)


show_boxplot(tmp_df, compart)


tmp_df = tmp_df.set_index(date)


# Additive Decomposition
plot_decomposition(tmp_df, compart)


# Test for stationarity
adf_test(tmp_df[compart].values)

ADF Statistic: -3.0623944710556987
p-value: 0.029464257418658487
Critical Values:
   1%, -3.4512146067362317
Critical Values:
   5%, -2.870730188960711
Critical Values:
   10%, -2.5716664849383113


# Test for trend stationarity
kpss_test(tmp_df[compart].values)

KPSS Statistic: 0.659024
p-value: 0.017271
Critical Values:
   10%, 0.347
Critical Values:
   5%, 0.463
Critical Values:
   2.5%, 0.574
Critical Values:
   1%, 0.739


# Detrend by subtracting best leastsq fit
plot_detrended_deseason(
    signal.detrend(tmp_df[compart].values), 
    province,
    compart,
    "Detrended")


# Detrend by subtracting trend comp
plot_detrended_deseason(
    remove_trend(tmp_df, compart), 
    province,
    compart,
    "Detrended")


plot_detrended_deseason_plotly(
    remove_trend(tmp_df, compart), 
    province,
    compart,
    "Detrended")


# Deseasonalize by subtracting trend
plot_detrended_deseason(
    deseason_trend(tmp_df, compart), 
    province,
    compart,
    "Deseasonalized")


# Deseasonalize by taking mov. avg. with length = seasonal window
plot_deseason_ma(tmp_df, compart, province)


# Seasonality test
plot_autocorr(tmp_df, compart)


# Autocorrelation and partial autocorrelation
plot_acf_pacf(tmp_df, compart)


"""
Lag plots:
If points get wide and scattered with increasing lag, 
this means lesser correlation
"""

plot_lag_plots(tmp_df.query("20200701 > Date"), compart)


plot_lag_plots(tmp_df, compart)


# Original Series
fig, axes = plt.subplots(3, 2, figsize=(15,12))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
axes[0, 0].xaxis.set_major_locator(locator)
axes[0, 0].xaxis.set_major_formatter(formatter)
axes[1, 0].xaxis.set_major_locator(locator)
axes[1, 0].xaxis.set_major_formatter(formatter)
axes[2, 0].xaxis.set_major_locator(locator)
axes[2, 0].xaxis.set_major_formatter(formatter)

axes[0, 0].plot(tmp_df.query("20200701 > Date")[compart])
axes[0, 0].set_title('Original Series')
plot_acf(tmp_df.query("20200701 > Date")[compart], ax=axes[0, 1])

# 1st Differencing
axes[1, 0].plot(tmp_df.query("20200701 > Date")[compart].diff())
axes[1, 0].set_title('1st Order Differencing')
plot_acf(tmp_df.query("20200701 > Date")[compart].diff().dropna(), ax=axes[1, 1])

# 2nd Differencing
axes[2, 0].plot(tmp_df.query("20200701 > Date")[compart].diff().diff())
axes[2, 0].set_title('2nd Order Differencing')
plot_acf(tmp_df.query("20200701 > Date")[compart].diff().diff().dropna(), ax=axes[2, 1])

plt.show()


# Estimate forecastability
print("SampEn:", SampEn(tmp_df[compart].values, m=2, r=0.2*np.std(tmp_df[compart].values)))
print("ApproxEn:", ApEn(tmp_df[compart].values, m=2, r=0.2*np.std(tmp_df[compart].values)))

SampEn: 0.08969363102750517
ApproxEn: 0.24777649675081914


# Smoothing
plot_smoothing(tmp_df, compart)


"""
Granger causality tests:

Infected - Month
Infected - Deaths
"""

tmp_df = covidpro_df[covidpro_df.Province == province]

tmp_df['month'] = tmp_df[date].dt.month
gc_res = grangercausalitytests(tmp_df[[compart, 'month']], maxlag=3)

Granger Causality
number of lags (no zero) 1
ssr based F test:         F=3.0126  , p=0.0837  , df_denom=286, df_num=1
ssr based chi2 test:   chi2=3.0442  , p=0.0810  , df=1
likelihood ratio test: chi2=3.0282  , p=0.0818  , df=1
parameter F test:         F=3.0126  , p=0.0837  , df_denom=286, df_num=1

Granger Causality
number of lags (no zero) 2
ssr based F test:         F=0.3696  , p=0.6914  , df_denom=283, df_num=2
ssr based chi2 test:   chi2=0.7522  , p=0.6865  , df=2
likelihood ratio test: chi2=0.7512  , p=0.6869  , df=2
parameter F test:         F=0.3696  , p=0.6914  , df_denom=283, df_num=2

Granger Causality
number of lags (no zero) 3
ssr based F test:         F=0.6856  , p=0.5615  , df_denom=280, df_num=3
ssr based chi2 test:   chi2=2.1082  , p=0.5502  , df=3
likelihood ratio test: chi2=2.1005  , p=0.5518  , df=3
parameter F test:         F=0.6856  , p=0.5615  , df_denom=280, df_num=3


gc_res = grangercausalitytests(tmp_df[[compart, 'Deaths']], maxlag=3)

Granger Causality
number of lags (no zero) 1
ssr based F test:         F=0.7995  , p=0.3720  , df_denom=286, df_num=1
ssr based chi2 test:   chi2=0.8079  , p=0.3688  , df=1
likelihood ratio test: chi2=0.8067  , p=0.3691  , df=1
parameter F test:         F=0.7995  , p=0.3720  , df_denom=286, df_num=1

Granger Causality
number of lags (no zero) 2
ssr based F test:         F=2.5788  , p=0.0776  , df_denom=283, df_num=2
ssr based chi2 test:   chi2=5.2488  , p=0.0725  , df=2
likelihood ratio test: chi2=5.2015  , p=0.0742  , df=2
parameter F test:         F=2.5788  , p=0.0776  , df_denom=283, df_num=2

Granger Causality
number of lags (no zero) 3
ssr based F test:         F=1.2330  , p=0.2980  , df_denom=280, df_num=3
ssr based chi2 test:   chi2=3.7915  , p=0.2849  , df=3
likelihood ratio test: chi2=3.7666  , p=0.2878  , df=3
parameter F test:         F=1.2330  , p=0.2980  , df_denom=280, df_num=3


province = "Firenze"
compart = "Deaths"
date = 'Date'


tmp_df = covidpro_df[covidpro_df.Province == province]


visualize_ts(tmp_df, date, compart, province)


show_boxplot(tmp_df, compart)


tmp_df = tmp_df.set_index(date)


# Additive Decomposition
plot_decomposition(tmp_df, compart)


# Test for stationarity
adf_test(tmp_df[compart].values)

ADF Statistic: -2.7519413702967155
p-value: 0.06547326647232678
Critial Values:
   1%, -3.45453261164607
Critial Values:
   5%, -2.8721859575020017
Critial Values:
   10%, -2.572442854861866


# Test for trend stationarity
kpss_test(tmp_df[compart].values)

KPSS Statistic: 0.365743
p-value: 0.091921
Critial Values:
   10%, 0.347
Critial Values:
   5%, 0.463
Critial Values:
   2.5%, 0.574
Critial Values:
   1%, 0.739


# Detrend by subtracting best leastsq fit
plot_detrended_deseason(
    signal.detrend(tmp_df[compart].values), 
    province,
    compart,
    "Detrended")


# Detrend by subtracting trend comp
plot_detrended_deseason(
    remove_trend(tmp_df, compart), 
    province,
    compart,
    "Detrended")


# Deseasonalize by subtracting trend
plot_detrended_deseason(
    deseason_trend(tmp_df, compart), 
    province,
    compart,
    "Deseasonalized")


# Deseasonalize by taking mov. avg. with length = seasonal window
plot_deseason_ma(tmp_df, compart, province)


# Seasonality test
plot_autocorr(tmp_df, compart)


# Autocorrelation and partial autocorrelation
plot_acf_pacf(tmp_df, compart)


"""
Lag plots:
If points get wide and scattered with increasing lag, 
this means lesser correlation
"""

plot_lag_plots(tmp_df, compart)


# Estimate forecastability
print("SampEn:", SampEn(tmp_df[compart].values, m=2, r=0.2*np.std(tmp_df[compart].values)))
print("ApproxEn:", ApEn(tmp_df[compart].values, m=2, r=0.2*np.std(tmp_df[compart].values)))

SampEn: 0.18732204802912877
ApproxEn: 0.47577134095104867


# Smoothing
plot_smoothing(tmp_df, compart)


"""
Granger causality tests:

Infected - Month
Infected - Deaths
"""

tmp_df = covidpro_df[covidpro_df.Province == province]

tmp_df['month'] = tmp_df[date].dt.month
gc_res = grangercausalitytests(tmp_df[[compart, 'month']], maxlag=3)

Granger Causality
number of lags (no zero) 1
ssr based F test:         F=2.8913  , p=0.0901  , df_denom=286, df_num=1
ssr based chi2 test:   chi2=2.9216  , p=0.0874  , df=1
likelihood ratio test: chi2=2.9069  , p=0.0882  , df=1
parameter F test:         F=2.8913  , p=0.0901  , df_denom=286, df_num=1

Granger Causality
number of lags (no zero) 2
ssr based F test:         F=1.6630  , p=0.1914  , df_denom=283, df_num=2
ssr based chi2 test:   chi2=3.3847  , p=0.1841  , df=2
likelihood ratio test: chi2=3.3649  , p=0.1859  , df=2
parameter F test:         F=1.6630  , p=0.1914  , df_denom=283, df_num=2

Granger Causality
number of lags (no zero) 3
ssr based F test:         F=1.0205  , p=0.3840  , df_denom=280, df_num=3
ssr based chi2 test:   chi2=3.1379  , p=0.3708  , df=3
likelihood ratio test: chi2=3.1209  , p=0.3734  , df=3
parameter F test:         F=1.0205  , p=0.3840  , df_denom=280, df_num=3


gc_res = grangercausalitytests(tmp_df[[compart, 'Deaths']], maxlag=3)

Granger Causality
number of lags (no zero) 1
ssr based F test:         F=0.0000  , p=1.0000  , df_denom=287, df_num=1
ssr based chi2 test:   chi2=0.0000  , p=1.0000  , df=1
likelihood ratio test: chi2=-0.0000 , p=1.0000  , df=1
parameter F test:         F=485.5733, p=0.0000  , df_denom=287, df_num=1

Granger Causality
number of lags (no zero) 2
ssr based F test:         F=0.0000  , p=1.0000  , df_denom=285, df_num=2
ssr based chi2 test:   chi2=0.0000  , p=1.0000  , df=2
likelihood ratio test: chi2=-0.0000 , p=1.0000  , df=2
parameter F test:         F=339.8168, p=0.0000  , df_denom=285, df_num=2

Granger Causality
number of lags (no zero) 3
ssr based F test:         F=-0.0000 , p=1.0000  , df_denom=283, df_num=3
ssr based chi2 test:   chi2=-0.0000 , p=1.0000  , df=3
likelihood ratio test: chi2=-0.0000 , p=1.0000  , df=3
parameter F test:         F=232.1738, p=0.0000  , df_denom=283, df_num=3


province = "Piemonte"
compart = "nuovi_positivi"
date = 'data'


tmp_df = dpc_regioni_df[dpc_regioni_df.denominazione_regione == province]


visualize_ts(tmp_df, date, compart, province)


show_boxplot(tmp_df, compart)


tmp_df = tmp_df.set_index(date)


# Additive Decomposition
plot_decomposition(tmp_df, compart)


# Test for stationarity
adf_test(tmp_df[compart].values)

ADF Statistic: -3.3560158064650696
p-value: 0.012552855296211371
Critial Values:
   1%, -3.4540935579190495
Critial Values:
   5%, -2.8719934111688965
Critial Values:
   10%, -2.5723401594120388


# Test for trend stationarity
kpss_test(tmp_df[compart].values)

KPSS Statistic: 0.703087
p-value: 0.013265
Critial Values:
   10%, 0.347
Critial Values:
   5%, 0.463
Critial Values:
   2.5%, 0.574
Critial Values:
   1%, 0.739


# Detrend by subtracting best leastsq fit
plot_detrended_deseason(
    signal.detrend(tmp_df[compart].values), 
    province,
    compart,
    "Detrended")


# Detrend by subtracting trend comp
plot_detrended_deseason(
    remove_trend(tmp_df, compart), 
    province,
    compart,
    "Detrended")


# Deseasonalize by subtracting trend
plot_detrended_deseason(
    deseason_trend(tmp_df, compart), 
    province,
    compart,
    "Deseasonalized")


# Deseasonalize by taking mov. avg. with length = seasonal window
plot_deseason_ma(tmp_df, compart, province)


# Seasonality test
plot_autocorr(tmp_df, compart)


# Autocorrelation and partial autocorrelation
plot_acf_pacf(tmp_df, compart)


"""
Lag plots:
If points get wide and scattered with increasing lag, 
this means lesser correlation
"""

plot_lag_plots(tmp_df, compart)


# Estimate forecastability
print("SampEn:", SampEn(tmp_df[compart].values, m=2, r=0.2*np.std(tmp_df[compart].values)))
print("ApproxEn:", ApEn(tmp_df[compart].values, m=2, r=0.2*np.std(tmp_df[compart].values)))

SampEn: 0.05778282138264353
ApproxEn: 0.22056687391795093


# Smoothing
plot_smoothing(tmp_df, compart)


"""
Granger causality tests:

Deaths - Month
Deaths - Infected
"""


tmp_df = dpc_regioni_df[dpc_regioni_df.denominazione_regione == province]

tmp_df['month'] = tmp_df[date].dt.month
gc_res = grangercausalitytests(tmp_df[[compart, 'month']], maxlag=3)

Granger Causality
number of lags (no zero) 1
ssr based F test:         F=2.8526  , p=0.0923  , df_denom=287, df_num=1
ssr based chi2 test:   chi2=2.8824  , p=0.0896  , df=1
likelihood ratio test: chi2=2.8682  , p=0.0903  , df=1
parameter F test:         F=2.8526  , p=0.0923  , df_denom=287, df_num=1

Granger Causality
number of lags (no zero) 2
ssr based F test:         F=1.0530  , p=0.3502  , df_denom=284, df_num=2
ssr based chi2 test:   chi2=2.1431  , p=0.3425  , df=2
likelihood ratio test: chi2=2.1352  , p=0.3438  , df=2
parameter F test:         F=1.0530  , p=0.3502  , df_denom=284, df_num=2

Granger Causality
number of lags (no zero) 3
ssr based F test:         F=1.2254  , p=0.3007  , df_denom=281, df_num=3
ssr based chi2 test:   chi2=3.7677  , p=0.2877  , df=3
likelihood ratio test: chi2=3.7433  , p=0.2906  , df=3
parameter F test:         F=1.2254  , p=0.3007  , df_denom=281, df_num=3


gc_res = grangercausalitytests(tmp_df[[compart, 'deceduti']], maxlag=3)

Granger Causality
number of lags (no zero) 1
ssr based F test:         F=0.0547  , p=0.8152  , df_denom=287, df_num=1
ssr based chi2 test:   chi2=0.0553  , p=0.8141  , df=1
likelihood ratio test: chi2=0.0553  , p=0.8141  , df=1
parameter F test:         F=0.0547  , p=0.8152  , df_denom=287, df_num=1

Granger Causality
number of lags (no zero) 2
ssr based F test:         F=0.0057  , p=0.9943  , df_denom=284, df_num=2
ssr based chi2 test:   chi2=0.0117  , p=0.9942  , df=2
likelihood ratio test: chi2=0.0117  , p=0.9942  , df=2
parameter F test:         F=0.0057  , p=0.9943  , df_denom=284, df_num=2

Granger Causality
number of lags (no zero) 3
ssr based F test:         F=0.0785  , p=0.9716  , df_denom=281, df_num=3
ssr based chi2 test:   chi2=0.2413  , p=0.9707  , df=3
likelihood ratio test: chi2=0.2412  , p=0.9707  , df=3
parameter F test:         F=0.0785  , p=0.9716  , df_denom=281, df_num=3


province = "Firenze"
compart = "New_cases"
date = 'Date'

tmp_df = covidpro_df[covidpro_df.Province == province]
tmp_df = tmp_df.set_index(date)


def mape(y_true, y_pred): 
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100


def adv_ma_plot(df, compart, window, plot_intervals=False, scale=1.96, plot_anomalies=False, show_anomalies_label=False, legend_position='upper left'):
    rolling_mean = df[[compart]].rolling(window=window).mean()

    plt.figure(figsize=(15,5))
    #plt.title("Moving average\n window size = {}".format(window))
    plt.plot(rolling_mean, "g", label="Rolling mean trend")

    if plot_intervals:
        mae = mean_absolute_error(df[[compart]][window:], rolling_mean[window:])
        deviation = np.std(df[[compart]][window:] - rolling_mean[window:])
        lower_bound = rolling_mean - (mae + scale * deviation)
        upper_bound = rolling_mean + (mae + scale * deviation)
        plt.plot(upper_bound, "r--", label="Upper Bound / Lower Bound")
        plt.plot(lower_bound, "r--")
        
        if plot_anomalies:
            
            anomalies = pd.DataFrame(index=df[[compart]].index, columns=df[[compart]].columns)
            anomalies[df[[compart]]<lower_bound] = df[[compart]][df[[compart]]<lower_bound]
            anomalies[df[[compart]]>upper_bound] = df[[compart]][df[[compart]]>upper_bound]
            plt.plot(anomalies, "ro", markersize=10)

            if show_anomalies_label:
                ymin, ymax = plt.ylim()
                plt.vlines(anomalies.dropna().index, ymin=ymin, ymax=ymax, linestyles='dashed', colors='grey')
                for x in anomalies.dropna().index:
                    plt.text(x, ymin + 20, x.strftime('%m-%d'), rotation=90, verticalalignment='center')
        
    plt.plot(df[[compart]][window:], label="Actual values")
    plt.legend(loc=legend_position)
    plt.show()


adv_ma_plot(tmp_df, compart, 7, plot_intervals=True, plot_anomalies=True)


adv_ma_plot(tmp_df, compart, 14, plot_intervals=True, plot_anomalies=True)


adv_ma_plot(tmp_df, compart, 30, plot_intervals=True, plot_anomalies=True)


province = "Firenze"
compart = "New_cases"
date = 'Date'

tmp_df = covidpro_df[covidpro_df.Province == province].query('20200701 > Date')
tmp_df = tmp_df.set_index(date)


adv_ma_plot(tmp_df, compart, 7, plot_intervals=True, plot_anomalies=True, show_anomalies_label=True, legend_position='upper right')


adv_ma_plot(tmp_df, compart, 14, plot_intervals=True, plot_anomalies=True, show_anomalies_label=True, legend_position='upper right')


adv_ma_plot(tmp_df, compart, 30, plot_intervals=True, plot_anomalies=True, show_anomalies_label=True, legend_position='upper right')


province = "Firenze"
compart = "New_cases"
date = 'Date'

tmp_df = covidpro_df[covidpro_df.Province == province].query('20201208 > Date > 20200701')
tmp_df = tmp_df.set_index(date)


adv_ma_plot(tmp_df, compart, 7, plot_intervals=True, plot_anomalies=True, show_anomalies_label=True, legend_position='upper left')


adv_ma_plot(tmp_df, compart, 14, plot_intervals=True, plot_anomalies=True, show_anomalies_label=True, legend_position='upper left')


adv_ma_plot(tmp_df, compart, 30, plot_intervals=True, plot_anomalies=True, show_anomalies_label=True, legend_position='upper left')


province = "Firenze"
compart = "New_cases"
date = 'Date'

tmp_df = covidpro_df[covidpro_df.Province == province].query('20200701 > Date')
tmp_df.loc[(tmp_df.Date == pd.Timestamp(2020, 4, 2)), "New_cases"] = np.nan
tmp_df["New_cases"].interpolate(inplace=True)
tmp_df.loc[(tmp_df.Date == pd.Timestamp(2020, 4, 2)), "New_cases"] = np.round(tmp_df.loc[(tmp_df.Date == pd.Timestamp(2020, 4, 2)), "New_cases"])
#tmp_df[compart] = tmp_df[compart].apply(lambda x: 0 if x is np.nan or x < 0 else x)
tmp_df.astype({"New_cases": "int32"})
tmp_df = tmp_df.set_index(date)


from statsmodels.tsa.holtwinters import ExponentialSmoothing, Holt

train = tmp_df[[compart]].query('20200615 > Date')
test = tmp_df[[compart]].query('20200615 <= Date')

model = ExponentialSmoothing(train[compart].values)
model_fit = model.fit()

yhat = model_fit.predict(start=0,end=len(test)-1)


print("MAE:", mean_absolute_error(test, yhat))
print("MSE:", mean_squared_error(test, yhat))
print("RMSE:", mean_squared_error(test, yhat, squared=False))

MAE: 2.0730830739525388
MSE: 6.975609362546363
RMSE: 2.6411378916191337


print("AIC:", model_fit.aic)
print("AICC:", model_fit.aicc)
print("BIC:", model_fit.bic)
print("k:", model_fit.k)
print("SSE:", model_fit.sse)
print("\n",model_fit.mle_retvals)

AIC: 656.2053176338434
AICC: 656.5791494095444
BIC: 661.6423153764335
k: 2
SSE: 37864.17282293216

      fun: 37864.17282293216
     jac: array([0.02880859, 0.00048828])
 message: 'Optimization terminated successfully.'
    nfev: 25
     nit: 5
    njev: 5
  status: 0
 success: True
       x: array([0.31869206, 1.05100326])


model_fit.params_formatted


#plt.figure(figsize=(8,5))
#plt.plot(train.index, model_fit.fittedvalues, label='Fitted')
#plt.plot(tmp_df.index, tmp_df[compart].values, label='Real')
#plt.plot(test.index, yhat, label='Predicted')
#plt.legend()
#plt.show()


fig, ax = plt.subplots(figsize=(8,5))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(train.index, model_fit.fittedvalues, label='Fitted')
ax.plot(tmp_df.index, tmp_df[compart].values, label='Real')
ax.plot(test.index, yhat, label='Predicted')
plt.legend()
plt.show()


model = Holt(train[compart].values)

# It works with Powell or leastsq, but not with
# the default L-BFGS-B
model_fit = model.fit(method='Powell')

yhat = model_fit.predict(start=0,end=len(test)-1)

print("AIC:", model_fit.aic)
print("AICC:", model_fit.aicc)
print("BIC:", model_fit.bic)
print("k:", model_fit.k)
print("SSE:", model_fit.sse)
print("\n",model_fit.mle_retvals)

AIC: 657.2857815834844
AICC: 658.0857815834844
BIC: 668.1597770686648
k: 4
SSE: 36889.909956354415

    direc: array([[ 0.        ,  0.        ,  0.        ,  1.        ],
       [-0.01065353,  0.0920848 ,  0.5055263 , -0.08930595],
       [ 0.        ,  0.        ,  1.        ,  0.        ],
       [-0.00874355,  0.17655601,  0.04365726, -0.28981009]])
     fun: 36889.909956354415
 message: 'Optimization terminated successfully.'
    nfev: 238
     nit: 5
  status: 0
 success: True
       x: array([ 0.15838621,  0.22455304, -4.26962293, -0.18676495])


print("MAE:", mean_absolute_error(test, yhat))
print("MSE:", mean_squared_error(test, yhat))
print("RMSE:", mean_squared_error(test, yhat, squared=False))

MAE: 3.468290108898218
MSE: 16.83948786329467
RMSE: 4.10359450522279


model_fit.params_formatted


#plt.figure(figsize=(8,5))
#plt.plot(train.index, model_fit.fittedvalues, label='Fitted')
#plt.plot(tmp_df.index, tmp_df[compart].values, label='Real')
#plt.plot(test.index, yhat, label='Predicted')
#plt.legend()
#plt.show()

fig, ax = plt.subplots(figsize=(8,5))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(train.index, model_fit.fittedvalues, label='Fitted')
ax.plot(tmp_df.index, tmp_df[compart].values, label='Real')
ax.plot(test.index, yhat, label='Predicted')
plt.legend()
plt.show()


model_es = ExponentialSmoothing(train[compart].values)
model_fit_es = model_es.fit()

yhat_es = model_fit_es.predict(start=0,end=len(test)-1)


#plt.figure(figsize=(8,5))
#plt.plot(train.index, model_fit.fittedvalues, label='Fitted (Holt)')
#plt.plot(test.index, yhat, label='Predicted (Holt)')
#plt.plot(train.index, model_fit_es.fittedvalues, label='Fitted (ExpSmt)')
#plt.plot(test.index, yhat_es, label='Predicted (ExpSmt)')
#plt.plot(tmp_df.index, tmp_df[compart].values, label='Real')
#plt.legend()
#plt.show()

fig, ax = plt.subplots(figsize=(8,5))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.scatter(tmp_df.index, tmp_df[compart].values, label='Real', s=4)
ax.plot(train.index, model_fit.fittedvalues, label='Fitted (Holt)', color="orange")
ax.plot(test.index, yhat, label='Predicted (Holt)', color="orange")
ax.plot(train.index, model_fit_es.fittedvalues, label='Fitted (ExpSmt)', color="red")
ax.plot(test.index, yhat_es, label='Predicted (ExpSmt)', color="red")
plt.legend()
plt.ylabel("Number of individuals")
plt.show()


tsplot(tmp_df[compart], lags=50)


adf_test(tmp_df[compart].values)
kpss_test(tmp_df[compart].values)

ADF Statistic: -0.9600587998949696
p-value: 0.7675518785663014
Critical Values:
   1%, -3.4851223522012855
Critical Values:
   5%, -2.88553750045158
Critical Values:
   10%, -2.5795685622144586

KPSS Statistic: 0.392363
p-value: 0.080447
Critical Values:
   10%, 0.347
Critical Values:
   5%, 0.463
Critical Values:
   2.5%, 0.574
Critical Values:
   1%, 0.739


res = tmp_df[compart] - tmp_df[compart].shift(1)
res.dropna().plot()
plt.show()


adf_test(res.dropna().values)
kpss_test(res.dropna().values)

ADF Statistic: -9.626634626858927
p-value: 1.6539339758754491e-16
Critical Values:
   1%, -3.4851223522012855
Critical Values:
   5%, -2.88553750045158
Critical Values:
   10%, -2.5795685622144586

KPSS Statistic: 0.211116
p-value: 0.100000
Critical Values:
   10%, 0.347
Critical Values:
   5%, 0.463
Critical Values:
   2.5%, 0.574
Critical Values:
   1%, 0.739
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/stattools.py:1876: InterpolationWarning:

The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is greater than the p-value returned.


res = np.log(tmp_df[compart]) - np.log(tmp_df[compart]).shift(1)

fig, ax = plt.subplots()
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(res.dropna())
#res.dropna().plot()
plt.show()


res_fix = res.replace([np.inf, -np.inf], np.nan).interpolate(method='time')
res_fix.plot()
plt.show()


# Shows that is stationary. Remember that KPSS null-hypo is opposite
# to ADF. We have to remove the trend and seasonality.
adf_test(res_fix.dropna().values)
kpss_test(res_fix.dropna().values)

ADF Statistic: -10.374148574924691
p-value: 2.224126550856314e-18
Critial Values:
   1%, -3.484219653271961
Critial Values:
   5%, -2.885145235641637
Critial Values:
   10%, -2.579359138917794

KPSS Statistic: 0.180195
p-value: 0.100000
Critial Values:
   10%, 0.347
Critial Values:
   5%, 0.463
Critial Values:
   2.5%, 0.574
Critial Values:
   1%, 0.739
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/stattools.py:1876: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is greater than the p-value returned.

  warnings.warn(warn_msg.format(direction="greater"), InterpolationWarning)


res_fix.dropna(inplace=True)


decomposed = seasonal_decompose(res_fix, model='additive', extrapolate_trend='freq')
plot_decomposition(result=decomposed)


detrended = res_fix - decomposed.trend
deseasonalized = detrended / decomposed.seasonal


fig, ax = plt.subplots()
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(deseasonalized)
plt.show()


tsplot(deseasonalized, lags=50)


adf_test(deseasonalized.values)
kpss_test(deseasonalized.values)

ADF Statistic: -10.589650606104959
p-value: 6.578190158075751e-19
Critial Values:
   1%, -3.4837793736959997
Critial Values:
   5%, -2.88495387648
Critial Values:
   10%, -2.579256976

KPSS Statistic: 0.138756
p-value: 0.100000
Critial Values:
   10%, 0.347
Critial Values:
   5%, 0.463
Critial Values:
   2.5%, 0.574
Critial Values:
   1%, 0.739
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/stattools.py:1876: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is greater than the p-value returned.

  warnings.warn(warn_msg.format(direction="greater"), InterpolationWarning)


model = AutoReg(train, lags=1)
model_fit = model.fit()

# make prediction
yhat = model_fit.predict(test.index[0], test.index[-1])

/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'


mean_absolute_error(test, yhat), mean_squared_error(test, yhat)

(27.37116829411773, 776.8755739975904)


fig, ax = plt.subplots(figsize=(8,5))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(model_fit.fittedvalues.index, model_fit.fittedvalues.values, label='Fitted')
ax.plot(tmp_df[compart].index, tmp_df[compart].values, label='Real')
ax.plot(test.index, yhat, label='Predicted')
plt.legend()
plt.show()


model_fit.plot_diagnostics(figsize=(10,8))
plt.plot()

[]


model_fit.summary()


model_fit.diagnostic_summary()


model_fit.conf_int()


model = ARIMA(train, order=(0, 0, 1))
model_fit = model.fit()

# make prediction
yhat = model_fit.predict(test.index[0], test.index[-1])

/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'


fig, ax = plt.subplots(figsize=(8,5))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(model_fit.fittedvalues.index, model_fit.fittedvalues.values, label='Fitted')
ax.plot(tmp_df[compart].index, tmp_df[compart].values, label='Real')
ax.plot(test.index, yhat, label='Predicted')
plt.legend()
plt.show()


model_fit.plot_diagnostics(figsize=(10,8))
plt.plot()

[]


mean_absolute_error(test, yhat), mean_squared_error(test, yhat)

(29.701556472778492, 890.4492769527631)


model_fit.summary()


model_fit.conf_int()


#ARMA
model = ARIMA(train, order=(2, 0, 1))
model_fit = model.fit()

# make prediction
yhat = model_fit.predict(test.index[0], test.index[-1])

/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'


fig, ax = plt.subplots(figsize=(8,5))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(model_fit.fittedvalues.index, model_fit.fittedvalues.values, label='Fitted')
ax.plot(tmp_df[compart].index, tmp_df[compart].values, label='Real')
ax.plot(test.index, yhat, label='Predicted')
plt.legend()
plt.show()


model_fit.plot_diagnostics(figsize=(10,8))
plt.plot()

[]


mean_absolute_error(test, yhat), mean_squared_error(test, yhat)

(9.202485412359536, 89.02252350369098)


model_fit.summary()


model_fit.conf_int()


#ARIMA
model = ARIMA(train, order=(1, 1, 1))
model_fit = model.fit()

# make prediction
yhat = model_fit.predict(test.index[0], test.index[-1])

/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'


fig, ax = plt.subplots(figsize=(8,5))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(model_fit.fittedvalues.index, model_fit.fittedvalues.values, label='Fitted')
ax.plot(tmp_df[compart].index, tmp_df[compart].values, label='Real')
ax.plot(test.index, yhat, label='Predicted')
plt.legend()
plt.show()


model_fit.plot_diagnostics(figsize=(10,8))
plt.plot()

[]


mean_absolute_error(test, yhat), mean_squared_error(test, yhat)

(3.62600149768879, 14.270879987640232)


model_fit.summary()


model_fit.conf_int()


res = np.log(tmp_df[compart]) - np.log(tmp_df[compart]).shift(1)
res_fix = res.replace([np.inf, -np.inf], np.nan).interpolate(method='time')
res_fix.dropna(inplace=True)
decomposed = seasonal_decompose(res_fix, model='additive', extrapolate_trend='freq')
detrended = res_fix - decomposed.trend
deseasonalized = detrended / decomposed.seasonal


train = deseasonalized[:'20200614']
test = deseasonalized['20200615':]


# fit model
model = AutoReg(train, lags=1)
model_fit = model.fit()

# make prediction
yhat = model_fit.predict(test.index[0], test.index[-1])

/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'


mean_absolute_error(test, yhat), mean_squared_error(test, yhat)

(1.757172058276709, 10.663912731295468)


fig, ax = plt.subplots(figsize=(8,5))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(model_fit.fittedvalues.index, model_fit.fittedvalues.values, label='Fitted')
ax.plot(deseasonalized.index, deseasonalized.values, label='Real')
ax.plot(test.index, yhat, label='Predicted')
plt.legend()
plt.show()


model_fit.plot_diagnostics(figsize=(10,8))
plt.plot()

[]


model_fit.summary()


model_fit.diagnostic_summary()


model_fit.conf_int()


model = ARIMA(train, order=(0, 0, 1))
model_fit = model.fit()

# make prediction
yhat = model_fit.predict(test.index[0], test.index[-1])

/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'


fig, ax = plt.subplots(figsize=(8,5))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(model_fit.fittedvalues.index, model_fit.fittedvalues.values, label='Fitted')
ax.plot(deseasonalized.index, deseasonalized.values, label='Real')
ax.plot(test.index, yhat, label='Predicted')
plt.legend()
plt.show()


model_fit.plot_diagnostics(figsize=(10,8))
plt.plot()

[]


mean_absolute_error(test, yhat), mean_squared_error(test, yhat)

(1.894738436825611, 11.226402830262469)


model_fit.summary()


model_fit.conf_int()


#ARMA
model = ARIMA(train, order=(2, 0, 1))
model_fit = model.fit()

# make prediction
yhat = model_fit.predict(test.index[0], test.index[-1])

/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'


fig, ax = plt.subplots(figsize=(8,5))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(model_fit.fittedvalues.index, model_fit.fittedvalues.values, label='Fitted')
ax.plot(deseasonalized.index, deseasonalized.values, label='Real')
ax.plot(test.index, yhat, label='Predicted')
plt.legend()
plt.show()


model_fit.plot_diagnostics(figsize=(10,8))
plt.plot()

[]


mean_absolute_error(test, yhat), mean_squared_error(test, yhat)

(1.8902241050586515, 11.22901271432867)


model_fit.summary()


model_fit.conf_int()


#ARIMA
model = ARIMA(train, order=(1, 1, 1))
model_fit = model.fit()

# make prediction
yhat = model_fit.predict(test.index[0], test.index[-1])

/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'


fig, ax = plt.subplots(figsize=(8,5))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(model_fit.fittedvalues.index, model_fit.fittedvalues.values, label='Fitted')
ax.plot(deseasonalized.index, deseasonalized.values, label='Real')
ax.plot(test.index, yhat, label='Predicted')
plt.legend()
plt.show()


model_fit.plot_diagnostics(figsize=(10,8))
plt.plot()

[]


mean_absolute_error(test, yhat), mean_squared_error(test, yhat)

(1.8951237943879946, 11.227053295988723)


model_fit.summary()


model_fit.conf_int()


# setting initial values and some bounds for them
from itertools import product

ps = list(range(2, 5)) + [28]
d=1 
qs = list(range(2, 5)) + [28]
Ps = range(0, 2)
D=1 
Qs = range(0, 2)
s = 7 # season length is 7

# creating list with all the possible combinations of parameters
parameters = product(ps, qs, Ps, Qs)
parameters_list = list(parameters)
len(parameters_list)

64


from tqdm import tqdm

def optimizeSARIMA(data, parameters_list, d, D, s):
    """
        Return dataframe with parameters and corresponding AIC
        
        parameters_list - list with (p, q, P, Q) tuples
        d - integration order in ARIMA model
        D - seasonal integration order 
        s - length of season
    """
    
    results = []
    best_aic = float("inf")

    for param in tqdm(parameters_list):
        # we need try-except because on some combinations model fails to converge
        try:
            model=sm.tsa.statespace.SARIMAX(data, order=(param[0], d, param[1]), 
                                            seasonal_order=(param[2], D, param[3], s)).fit(disp=-1)
        except:
            continue
        aic = model.aic
        # saving best model, AIC and parameters
        if aic < best_aic:
            best_model = model
            best_aic = aic
            best_param = param
        results.append([param, model.aic])

    result_table = pd.DataFrame(results)
    result_table.columns = ['parameters', 'aic']
    # sorting in ascending order, the lower AIC is - the better
    result_table = result_table.sort_values(by='aic', ascending=True).reset_index(drop=True)
    
    return result_table


import warnings
warnings.filterwarnings('ignore')


result_table = optimizeSARIMA(deseasonalized, parameters_list, d, D, s)

100%|██████████| 64/64 [07:31<00:00,  7.05s/it]


warnings.filterwarnings('default')


result_table.head()


#p, q, P, Q = result_table.parameters[0]
p, q, P, Q = (2, 3, 1, 1)

best_results = sm.tsa.statespace.SARIMAX(deseasonalized, order=(p, d, q), 
                                        seasonal_order=(P, D, Q, s)).fit(disp=-1)
print(best_results.summary())

/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:524: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  warnings.warn('No frequency information was'
                                      SARIMAX Results                                      
===========================================================================================
Dep. Variable:                                   y   No. Observations:                  126
Model:             SARIMAX(2, 1, 3)x(1, 1, [1], 7)   Log Likelihood                -400.553
Date:                             Fri, 11 Dec 2020   AIC                            817.105
Time:                                     16:11:14   BIC                            839.270
Sample:                                 02-26-2020   HQIC                           826.105
                                      - 06-30-2020                                         
Covariance Type:                               opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
ar.L1         -1.5240      0.096    -15.919      0.000      -1.712      -1.336
ar.L2         -0.9087      0.077    -11.786      0.000      -1.060      -0.758
ma.L1          0.6194      7.419      0.083      0.933     -13.922      15.160
ma.L2         -0.6318     12.099     -0.052      0.958     -24.346      23.083
ma.L3         -0.9870      7.439     -0.133      0.894     -15.567      13.593
ar.S.L7       -0.2512      0.082     -3.073      0.002      -0.411      -0.091
ma.S.L7       -0.6741      0.079     -8.501      0.000      -0.830      -0.519
sigma2        44.1598    330.969      0.133      0.894    -604.529     692.848
===================================================================================
Ljung-Box (L1) (Q):                   0.21   Jarque-Bera (JB):                22.31
Prob(Q):                              0.65   Prob(JB):                         0.00
Heteroskedasticity (H):               0.94   Skew:                            -0.31
Prob(H) (two-sided):                  0.86   Kurtosis:                         5.04
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
/home/nick/anaconda3/lib/python3.8/site-packages/statsmodels/base/model.py:566: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "


tsplot(best_results.resid, lags=50)


best_results.plot_diagnostics(figsize=(10,8))
plt.show()


best_results.conf_int()


print("MAE:", best_results.mae)
print("MSE:", best_results.mse)
print("SSE:", best_results.sse)

MAE: 4.981802952314746
MSE: 54.63265256729769
SSE: 6883.714223479509


def plotSARIMA(y_train, y_test, model, s, d):
    """
        Plots model vs predicted values
        
        series - dataset with timeseries
        model - fitted SARIMA model
        n_steps - number of steps to predict in the future
        
    """
    # adding model values
    fitted = model.fittedvalues[s+d:].copy()
    real = y_train[s+d:].copy()

    real_plus_test = pd.concat([real, y_test])
    forecast = model.predict(start=real.index[-1], end=real_plus_test.index[-1])
    fitted_plus_prediction = pd.concat([fitted, forecast])

    fig, ax = plt.subplots(figsize=(15, 7))
    locator = mdates.AutoDateLocator(minticks=3)
    formatter = mdates.ConciseDateFormatter(locator)
    ax.xaxis.set_major_locator(locator)
    ax.xaxis.set_major_formatter(formatter)
    ax.plot(fitted_plus_prediction, label="model")
    plt.axvspan(fitted.index[-1], fitted_plus_prediction.index[-1], alpha=0.5, color='lightgrey')
    ax.plot(real_plus_test, label="actual")

    #plt.figure(figsize=(15, 7))
    #plt.plot(fitted_plus_prediction, label="model")
    #plt.axvspan(fitted.index[-1], fitted_plus_prediction.index[-1], alpha=0.5, color='lightgrey')
    #plt.plot(real_plus_test, label="actual")
    plt.legend(loc='upper right')
    plt.show()


test_df = covidpro_df[covidpro_df.Province == province].query('20200715 > Date >= 20200701')
test_df[compart] = test_df[compart].apply(lambda x: 0 if x is np.nan or x < 0 else x)
test_df = test_df.set_index(date)

test_df = test_df[[compart]]


plotSARIMA(deseasonalized, test_df[[compart]][compart], best_results, s, d)


import pmdarima as pm
from pmdarima.arima.utils import nsdiffs, ndiffs
from pmdarima.arima import ADFTest
from pmdarima import model_selection


province = "Firenze"
compart = "New_cases"
date = 'Date'

tmp_df = covidpro_df[covidpro_df.Province == province].query('20200701 > Date')
tmp_df.loc[(tmp_df.Date == pd.Timestamp(2020, 4, 2)), "New_cases"] = np.nan
tmp_df["New_cases"].interpolate(inplace=True)
tmp_df.loc[(tmp_df.Date == pd.Timestamp(2020, 4, 2)), "New_cases"] = np.round(tmp_df.loc[(tmp_df.Date == pd.Timestamp(2020, 4, 2)), "New_cases"])
#tmp_df[compart] = tmp_df[compart].apply(lambda x: 0 if x is np.nan or x < 0 else x)
tmp_df.astype({"New_cases": "int32"})
tmp_df = tmp_df.set_index(date)


train = tmp_df[[compart]].query('20200615 > Date')
test = tmp_df[[compart]].query('20200615 <= Date')


adf_test = ADFTest()
adf_test.should_diff(tmp_df[compart])

(0.552244669974572, True)


ndiffs(tmp_df[compart], test='adf', max_d=5), ndiffs(tmp_df[compart], test='kpss', max_d=5)

(1, 1)


nsdiffs(
    tmp_df[compart],
    m=7,
    max_D=30,
    test='ch')

0


nsdiffs(
    tmp_df[compart],
    m=7,
    max_D=30,
    test='ocsb')

0


smodel = pm.auto_arima(train, start_p=1, start_q=1,
                         test='adf',
                         max_p=14, max_q=14, m=7,
                         start_P=0, seasonal=True,
                         trace=True,
                         d=1, D=0,
                         stepwise=True, n_jobs=-1)

Performing stepwise search to minimize aic
 ARIMA(1,1,1)(0,0,1)[7] intercept   : AIC=966.720, Time=0.78 sec
 ARIMA(0,1,0)(0,0,0)[7] intercept   : AIC=993.029, Time=0.02 sec
 ARIMA(1,1,0)(1,0,0)[7] intercept   : AIC=987.302, Time=0.28 sec
 ARIMA(0,1,1)(0,0,1)[7] intercept   : AIC=967.243, Time=0.36 sec
 ARIMA(0,1,0)(0,0,0)[7]             : AIC=991.029, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[7] intercept   : AIC=967.654, Time=0.10 sec
 ARIMA(1,1,1)(1,0,1)[7] intercept   : AIC=963.649, Time=1.03 sec
 ARIMA(1,1,1)(1,0,0)[7] intercept   : AIC=965.673, Time=0.50 sec
 ARIMA(1,1,1)(2,0,1)[7] intercept   : AIC=965.111, Time=0.76 sec
 ARIMA(1,1,1)(1,0,2)[7] intercept   : AIC=964.961, Time=0.85 sec
 ARIMA(1,1,1)(0,0,2)[7] intercept   : AIC=966.296, Time=0.91 sec
 ARIMA(1,1,1)(2,0,0)[7] intercept   : AIC=964.572, Time=0.93 sec
 ARIMA(1,1,1)(2,0,2)[7] intercept   : AIC=inf, Time=3.51 sec
 ARIMA(0,1,1)(1,0,1)[7] intercept   : AIC=964.281, Time=0.83 sec
 ARIMA(1,1,0)(1,0,1)[7] intercept   : AIC=984.296, Time=1.09 sec
 ARIMA(2,1,1)(1,0,1)[7] intercept   : AIC=961.473, Time=2.30 sec
 ARIMA(2,1,1)(0,0,1)[7] intercept   : AIC=964.377, Time=1.44 sec
 ARIMA(2,1,1)(1,0,0)[7] intercept   : AIC=963.634, Time=1.32 sec
 ARIMA(2,1,1)(2,0,1)[7] intercept   : AIC=962.361, Time=2.04 sec
 ARIMA(2,1,1)(1,0,2)[7] intercept   : AIC=961.983, Time=1.70 sec
 ARIMA(2,1,1)(0,0,0)[7] intercept   : AIC=964.268, Time=0.25 sec
 ARIMA(2,1,1)(0,0,2)[7] intercept   : AIC=963.374, Time=1.70 sec
 ARIMA(2,1,1)(2,0,0)[7] intercept   : AIC=962.007, Time=0.96 sec
 ARIMA(2,1,1)(2,0,2)[7] intercept   : AIC=inf, Time=3.27 sec
 ARIMA(2,1,0)(1,0,1)[7] intercept   : AIC=976.313, Time=1.01 sec
 ARIMA(3,1,1)(1,0,1)[7] intercept   : AIC=958.527, Time=1.31 sec
 ARIMA(3,1,1)(0,0,1)[7] intercept   : AIC=962.315, Time=0.91 sec
 ARIMA(3,1,1)(1,0,0)[7] intercept   : AIC=960.676, Time=0.95 sec
 ARIMA(3,1,1)(2,0,1)[7] intercept   : AIC=960.054, Time=1.83 sec
 ARIMA(3,1,1)(1,0,2)[7] intercept   : AIC=959.930, Time=1.89 sec
 ARIMA(3,1,1)(0,0,0)[7] intercept   : AIC=964.009, Time=0.29 sec
 ARIMA(3,1,1)(0,0,2)[7] intercept   : AIC=961.135, Time=1.48 sec
 ARIMA(3,1,1)(2,0,0)[7] intercept   : AIC=959.173, Time=1.83 sec
 ARIMA(3,1,1)(2,0,2)[7] intercept   : AIC=inf, Time=4.11 sec
 ARIMA(3,1,0)(1,0,1)[7] intercept   : AIC=961.389, Time=1.68 sec
 ARIMA(4,1,1)(1,0,1)[7] intercept   : AIC=960.480, Time=1.30 sec
 ARIMA(3,1,2)(1,0,1)[7] intercept   : AIC=955.802, Time=2.13 sec
 ARIMA(3,1,2)(0,0,1)[7] intercept   : AIC=959.180, Time=1.31 sec
 ARIMA(3,1,2)(1,0,0)[7] intercept   : AIC=957.334, Time=1.37 sec
 ARIMA(3,1,2)(2,0,1)[7] intercept   : AIC=957.658, Time=3.67 sec
 ARIMA(3,1,2)(1,0,2)[7] intercept   : AIC=957.608, Time=3.67 sec
 ARIMA(3,1,2)(0,0,0)[7] intercept   : AIC=962.585, Time=0.29 sec
 ARIMA(3,1,2)(0,0,2)[7] intercept   : AIC=958.924, Time=1.38 sec
 ARIMA(3,1,2)(2,0,0)[7] intercept   : AIC=956.791, Time=2.01 sec
 ARIMA(3,1,2)(2,0,2)[7] intercept   : AIC=958.160, Time=3.72 sec
 ARIMA(2,1,2)(1,0,1)[7] intercept   : AIC=966.163, Time=1.38 sec
 ARIMA(4,1,2)(1,0,1)[7] intercept   : AIC=957.778, Time=1.31 sec
 ARIMA(3,1,3)(1,0,1)[7] intercept   : AIC=957.188, Time=2.28 sec
 ARIMA(2,1,3)(1,0,1)[7] intercept   : AIC=956.379, Time=2.58 sec
 ARIMA(4,1,3)(1,0,1)[7] intercept   : AIC=956.897, Time=3.36 sec
 ARIMA(3,1,2)(1,0,1)[7]             : AIC=953.834, Time=1.59 sec
 ARIMA(3,1,2)(0,0,1)[7]             : AIC=957.187, Time=1.05 sec
 ARIMA(3,1,2)(1,0,0)[7]             : AIC=955.342, Time=0.79 sec
 ARIMA(3,1,2)(2,0,1)[7]             : AIC=955.691, Time=2.22 sec
 ARIMA(3,1,2)(1,0,2)[7]             : AIC=955.641, Time=1.64 sec
 ARIMA(3,1,2)(0,0,0)[7]             : AIC=960.590, Time=0.20 sec
 ARIMA(3,1,2)(0,0,2)[7]             : AIC=956.931, Time=1.71 sec
 ARIMA(3,1,2)(2,0,0)[7]             : AIC=954.806, Time=1.37 sec
 ARIMA(3,1,2)(2,0,2)[7]             : AIC=956.189, Time=3.61 sec
 ARIMA(2,1,2)(1,0,1)[7]             : AIC=964.192, Time=1.84 sec
 ARIMA(3,1,1)(1,0,1)[7]             : AIC=956.558, Time=0.98 sec
 ARIMA(4,1,2)(1,0,1)[7]             : AIC=955.810, Time=1.29 sec
 ARIMA(3,1,3)(1,0,1)[7]             : AIC=955.217, Time=1.65 sec
 ARIMA(2,1,1)(1,0,1)[7]             : AIC=959.503, Time=0.77 sec
 ARIMA(2,1,3)(1,0,1)[7]             : AIC=954.412, Time=1.49 sec
 ARIMA(4,1,1)(1,0,1)[7]             : AIC=958.511, Time=1.05 sec
 ARIMA(4,1,3)(1,0,1)[7]             : AIC=954.908, Time=2.15 sec

Best model:  ARIMA(3,1,2)(1,0,1)[7]          
Total fit time: 101.505 seconds


smodel.summary()

/home/nick/anaconda3/lib/python3.8/site-packages/ipykernel/ipkernel.py:283: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)


smodel.plot_diagnostics(figsize=(10,8))
plt.plot()

[]


yhat, ci = smodel.predict(n_periods=len(test), return_conf_int=True)

/home/nick/anaconda3/lib/python3.8/site-packages/ipykernel/ipkernel.py:283: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)


mean_absolute_error(test, yhat), mean_squared_error(test, yhat)

/home/nick/anaconda3/lib/python3.8/site-packages/ipykernel/ipkernel.py:283: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)

(3.076240754327265, 11.238184494484766)


lower_series = pd.Series(ci[:, 0], index=test.index)
upper_series = pd.Series(ci[:, 1], index=test.index)

fig, ax = plt.subplots(figsize=(9,6))
locator = mdates.AutoDateLocator(minticks=3)
formatter = mdates.ConciseDateFormatter(locator)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.plot(train.index, train.values, label='Train')
ax.plot(test.index, yhat, label='Predicted')
ax.plot(test.index, test.values, label='Test')
plt.fill_between(lower_series.index, 
                 lower_series, 
                 upper_series, 
                 color='k', alpha=.15)
plt.legend()
plt.show()


smodel.order, smodel.seasonal_order

/home/nick/anaconda3/lib/python3.8/site-packages/ipykernel/ipkernel.py:283: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)

((3, 1, 2), (1, 0, 1, 7))


est = pm.ARIMA(order=smodel.order,
               seasonal_order=smodel.seasonal_order,
               suppress_warnings=True)
cv = model_selection.SlidingWindowForecastCV(window_size=7, step=1, h=7)
predictions = model_selection.cross_val_predict(
    est, tmp_df[compart], cv=cv, verbose=2, averaging="median")

# plot the predictions over the original series
x_axis = np.arange(tmp_df[compart].shape[0])
n_test = predictions.shape[0]

plt.plot(x_axis, tmp_df[compart], alpha=0.75, c='b')
plt.plot(x_axis[-n_test:], predictions, alpha=0.75, c='g')  # Forecasts
plt.title("Cross-validated forecasts")
plt.show()

/home/nick/anaconda3/lib/python3.8/site-packages/ipykernel/ipkernel.py:283: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
[CV] fold=0 ..........................................................
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model1_cv_scores = model_selection.cross_val_score(
    smodel, test, scoring='mean_squared_error', cv=cv, verbose=2)

/home/nick/anaconda3/lib/python3.8/site-packages/ipykernel/ipkernel.py:283: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
[CV] fold=0 ..........................................................
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[CV] fold=2 ..........................................................


model1_cv_scores

/home/nick/anaconda3/lib/python3.8/site-packages/ipykernel/ipkernel.py:283: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)

array([1.25279535, 0.58223369, 1.08500275])


np.average(model1_cv_scores)

0.9733439315665073


prov_auto_sarimax = {}
aics, maes, mses, orders, sorders, cv_scores = [], [], [], [], [], []
from tqdm import tqdm
for province in tqdm(covidpro_df.Province.unique()):
    compart = "New_cases"
    date = 'Date'

    tmp_df = covidpro_df[covidpro_df.Province == province].query('20200701 > Date')
    tmp_df = tmp_df.set_index(date)

    train = tmp_df[[compart]].query('20200615 > Date')
    test = tmp_df[[compart]].query('20200615 <= Date')

    smodel = pm.auto_arima(
        train, start_p=1, start_q=1,
        test='adf', m=7, seasonal=True,
        stepwise=True, n_jobs=-1)
    
    cv = model_selection.SlidingWindowForecastCV(window_size=7, step=7, h=7)
    cv_model_scores = model_selection.cross_val_score(smodel, test, scoring='mean_squared_error', cv=cv, verbose=0)

    cv_scores.append(np.average(cv_model_scores))

    aics.append(smodel.aic())
    orders.append(smodel.order)
    sorders.append(smodel.seasonal_order)
    
    yhat, ci = smodel.predict(n_periods=len(test), return_conf_int=True)
    maes.append(mean_absolute_error(test, yhat))
    mses.append(mean_squared_error(test, yhat))

prov_auto_sarimax["Province"] = covidpro_df.Province.unique()
prov_auto_sarimax["AIC"] = np.round(aics, 2)
prov_auto_sarimax["MSE"] = np.round(mses, 2)
prov_auto_sarimax["MAE"] = np.round(maes, 2)
prov_auto_sarimax["CV_MSE"] = np.round(cv_scores, 2)
prov_auto_sarimax["Order"] = orders
prov_auto_sarimax["Season_Order"] = sorders

100%|██████████| 91/91 [19:05<00:00, 12.59s/it]


prov_df_res = pd.DataFrame.from_dict(prov_auto_sarimax)
prov_df_res


print(prov_df_res.to_latex(index=False))

\begin{tabular}{lrrrrll}
\toprule
              Province &      AIC &      MSE &    MAE &    CV\_MSE &      Order &  Season\_Order \\
\midrule
             Agrigento &   503.72 &     0.00 &   0.00 &      0.00 &  (2, 1, 1) &  (0, 0, 0, 7) \\
           Alessandria &  1101.68 &    68.62 &   7.24 &    148.68 &  (0, 1, 1) &  (0, 0, 0, 7) \\
                Ancona &   853.51 &     0.79 &   0.87 &      0.16 &  (1, 1, 2) &  (2, 0, 0, 7) \\
                 Aosta &   889.98 &     0.33 &   0.33 &      0.37 &  (1, 1, 1) &  (0, 0, 1, 7) \\
                Arezzo &   807.62 &     2.51 &   1.12 &      1.83 &  (1, 1, 2) &  (0, 0, 0, 7) \\
         Ascoli Piceno &   668.07 &     0.00 &   0.00 &      0.00 &  (2, 1, 1) &  (0, 0, 2, 7) \\
                  Asti &   905.75 &     1.80 &   1.06 &      0.56 &  (0, 1, 2) &  (0, 0, 0, 7) \\
                  Bari &   834.38 &     0.17 &   0.21 &      0.63 &  (0, 1, 1) &  (0, 0, 0, 7) \\
 Barletta-Andria-Trani &   722.12 &     0.00 &   0.00 &      0.00 &  (1, 1, 2) &  (0, 0, 0, 7) \\
               Belluno &   831.96 &     1.14 &   0.83 &      3.57 &  (0, 1, 1) &  (0, 0, 0, 7) \\
                Biella &   824.66 &     0.51 &   0.68 &      0.86 &  (1, 1, 1) &  (0, 0, 0, 7) \\
               Bologna &   976.31 &    69.62 &   7.13 &    104.67 &  (2, 1, 0) &  (2, 0, 0, 7) \\
               Bolzano &   971.26 &     7.05 &   1.74 &     17.36 &  (0, 1, 1) &  (0, 0, 1, 7) \\
              Brindisi &   673.33 &     0.45 &   0.44 &      0.21 &  (0, 1, 1) &  (1, 0, 1, 7) \\
              Cagliari &   534.34 &     0.15 &   0.31 &      0.43 &  (0, 1, 1) &  (0, 0, 2, 7) \\
         Caltanissetta &   500.07 &     4.12 &   0.63 &      2.10 &  (0, 1, 3) &  (0, 0, 0, 7) \\
            Campobasso &   662.51 &     0.16 &   0.24 &      0.29 &  (0, 1, 1) &  (0, 0, 0, 7) \\
               Catania &   790.07 &     0.31 &   0.37 &      0.08 &  (1, 1, 2) &  (0, 0, 0, 7) \\
             Catanzaro &   723.46 &     0.00 &   0.01 &      0.00 &  (1, 0, 1) &  (0, 0, 0, 7) \\
                Chieti &   817.61 &     0.26 &   0.51 &      0.29 &  (0, 1, 1) &  (0, 0, 0, 7) \\
               Cosenza &   688.11 &     0.00 &   0.00 &      0.00 &  (4, 1, 2) &  (0, 0, 0, 7) \\
               Cremona &  1199.33 &    39.32 &   5.87 &     10.89 &  (0, 1, 2) &  (0, 0, 1, 7) \\
               Crotone &   502.94 &     0.13 &   0.13 &      0.23 &  (0, 1, 2) &  (1, 0, 0, 7) \\
                 Cuneo &   998.37 &    10.43 &   3.00 &      2.71 &  (2, 1, 1) &  (0, 0, 1, 7) \\
                  Enna &   679.73 &    10.56 &   0.81 &     28.09 &  (2, 1, 1) &  (1, 0, 0, 7) \\
                 Fermo &   707.35 &     0.36 &   0.53 &      0.57 &  (3, 1, 0) &  (1, 0, 0, 7) \\
               Ferrara &   867.02 &    11.87 &   2.36 &     28.02 &  (0, 1, 1) &  (1, 0, 0, 7) \\
               Firenze &  1043.93 &    14.92 &   3.70 &      1.14 &  (2, 1, 1) &  (0, 0, 0, 7) \\
                Foggia &   801.01 &     0.75 &   0.62 &      1.77 &  (0, 1, 1) &  (0, 0, 0, 7) \\
          Forli-Cesena &   857.98 &    10.63 &   1.96 &     20.97 &  (0, 1, 1) &  (0, 0, 0, 7) \\
             Frosinone &   745.20 &    90.27 &   2.69 &    206.43 &  (0, 1, 1) &  (1, 0, 0, 7) \\
                Genova &  1312.66 &    24.58 &   4.59 &     19.26 &  (0, 1, 1) &  (0, 0, 0, 7) \\
               Gorizia &   523.08 &     0.06 &   0.14 &      0.00 &  (1, 1, 1) &  (0, 0, 0, 7) \\
              Grosseto &   761.54 &     0.24 &   0.49 &      0.29 &  (1, 1, 1) &  (0, 0, 0, 7) \\
               Imperia &  1127.37 &     7.05 &   2.59 &      0.30 &  (0, 1, 1) &  (0, 0, 0, 7) \\
               Isernia &   528.44 &     0.41 &   0.60 &      0.49 &  (1, 0, 0) &  (0, 0, 0, 7) \\
              L'Aquila &   544.03 &     0.18 &   0.39 &      0.14 &  (4, 1, 4) &  (0, 0, 0, 7) \\
             La Spezia &   955.66 &     1.62 &   1.07 &      0.31 &  (2, 1, 3) &  (0, 0, 0, 7) \\
                Latina &   817.92 &   147.11 &   3.77 &    334.84 &  (0, 1, 1) &  (0, 0, 0, 7) \\
                 Lecce &   734.84 &     0.12 &   0.13 &      0.14 &  (2, 1, 1) &  (0, 0, 0, 7) \\
               Livorno &   777.23 &     0.98 &   0.94 &      0.18 &  (1, 1, 2) &  (1, 0, 1, 7) \\
                 Lucca &   925.65 &     0.32 &   0.39 &      0.28 &  (0, 1, 2) &  (0, 0, 0, 7) \\
              Macerata &   796.67 &     2.84 &   1.51 &      3.79 &  (0, 1, 1) &  (0, 0, 0, 7) \\
         Massa Carrara &   911.35 &     0.11 &   0.26 &      0.14 &  (0, 1, 1) &  (0, 0, 0, 7) \\
                Matera &   544.88 &     0.07 &   0.14 &      0.00 &  (3, 1, 0) &  (0, 0, 1, 7) \\
               Messina &   759.13 &     0.43 &   0.32 &      0.15 &  (1, 1, 2) &  (0, 0, 0, 7) \\
                Modena &   978.61 &   105.07 &   3.29 &    226.13 &  (3, 1, 2) &  (0, 0, 0, 7) \\
                Novara &  1075.70 &    25.37 &   2.93 &      3.29 &  (0, 1, 1) &  (1, 0, 0, 7) \\
                 Nuoro &   560.70 &     0.53 &   0.72 &      0.02 &  (0, 0, 0) &  (0, 0, 0, 7) \\
              Oristano &   366.05 &     0.11 &   0.17 &      0.08 &  (0, 1, 1) &  (0, 0, 0, 7) \\
                Padova &   947.65 &     4.91 &   1.84 &      1.71 &  (4, 1, 0) &  (0, 0, 2, 7) \\
               Palermo &   723.45 &     1.73 &   1.23 &      0.23 &  (2, 1, 1) &  (0, 0, 0, 7) \\
                 Parma &  1027.27 &    19.64 &   3.86 &     26.00 &  (0, 1, 1) &  (0, 0, 0, 7) \\
               Perugia &   784.18 &     0.07 &   0.09 &      0.02 &  (1, 1, 0) &  (0, 0, 1, 7) \\
       Pesaro e Urbino &   925.82 &     0.20 &   0.31 &      0.43 &  (0, 1, 1) &  (0, 0, 0, 7) \\
               Pescara &   845.09 &   104.26 &   3.60 &    254.35 &  (1, 1, 2) &  (0, 0, 0, 7) \\
              Piacenza &  1006.70 &    47.70 &   2.77 &    117.82 &  (2, 1, 0) &  (1, 0, 0, 7) \\
                  Pisa &   759.75 &    40.19 &   2.06 &     86.62 &  (2, 1, 0) &  (0, 0, 0, 7) \\
               Pistoia &   727.45 &   244.01 &   4.45 &    551.57 &  (1, 1, 2) &  (1, 0, 2, 7) \\
             Pordenone &   780.26 &     0.53 &   0.65 &      0.55 &  (0, 1, 1) &  (0, 0, 0, 7) \\
               Potenza &   544.48 &     0.00 &   0.01 &      0.00 &  (0, 1, 2) &  (0, 0, 0, 7) \\
                 Prato &   708.44 &     0.85 &   0.55 &      1.28 &  (2, 1, 3) &  (0, 0, 0, 7) \\
                Ragusa &   456.26 &     0.70 &   0.83 &      0.00 &  (1, 0, 0) &  (0, 0, 0, 7) \\
               Ravenna &   810.43 &     3.90 &   1.21 &      8.67 &  (0, 1, 1) &  (0, 0, 0, 7) \\
    Reggio di Calabria &   646.99 &     3.31 &   1.06 &     27.43 &  (0, 1, 1) &  (0, 0, 0, 7) \\
    Reggio nell'Emilia &  1087.93 &    38.35 &   3.09 &     62.33 &  (0, 1, 1) &  (1, 0, 1, 7) \\
                 Rieti &   824.55 &    15.43 &   3.37 &     28.00 &  (1, 1, 5) &  (0, 0, 0, 7) \\
                Rimini &   925.73 &     7.61 &   1.52 &     20.04 &  (0, 1, 2) &  (1, 0, 0, 7) \\
                  Roma &   955.52 &    97.44 &   9.03 &     26.51 &  (0, 1, 1) &  (0, 0, 0, 7) \\
                Rovigo &   686.60 &     0.27 &   0.34 &      0.57 &  (0, 1, 1) &  (2, 0, 0, 7) \\
               Sassari &   874.67 &     0.38 &   0.57 &      0.08 &  (0, 1, 1) &  (0, 0, 0, 7) \\
                Savona &  1190.88 &   282.92 &  16.80 &      0.43 &  (0, 0, 0) &  (0, 0, 0, 7) \\
                 Siena &   703.72 &     0.40 &   0.58 &      0.00 &  (1, 1, 2) &  (0, 0, 1, 7) \\
              Siracusa &   584.06 &   297.22 &   4.41 &      0.14 &  (0, 1, 1) &  (0, 0, 0, 7) \\
          Sud Sardegna &   562.75 &     0.70 &   0.79 &      0.12 &  (0, 0, 1) &  (0, 0, 0, 7) \\
               Taranto &   568.05 &     0.06 &   0.06 &      0.14 &  (1, 1, 1) &  (0, 0, 0, 7) \\
                Teramo &   784.61 &     1.46 &   1.14 &      0.29 &  (0, 1, 2) &  (1, 0, 0, 7) \\
                 Terni &   623.32 &     0.17 &   0.38 &      0.14 &  (1, 1, 2) &  (0, 0, 0, 7) \\
                Torino &  1267.17 &   139.37 &  10.82 &   1177.79 &  (1, 1, 1) &  (1, 0, 0, 7) \\
               Trapani &   465.40 &     0.07 &   0.10 &      0.08 &  (1, 1, 2) &  (0, 0, 2, 7) \\
                Trento &  1051.61 &  9276.93 &  25.76 &  21119.99 &  (0, 1, 1) &  (1, 0, 0, 7) \\
               Treviso &   994.43 &     0.73 &   0.66 &      1.22 &  (1, 1, 1) &  (1, 0, 0, 7) \\
               Trieste &   873.86 &     0.39 &   0.62 &      0.00 &  (0, 1, 1) &  (0, 0, 0, 7) \\
                 Udine &   865.11 &     0.26 &   0.51 &      0.00 &  (1, 1, 1) &  (0, 0, 0, 7) \\
               Venezia &   960.00 &     3.36 &   1.76 &      0.21 &  (0, 1, 1) &  (0, 0, 1, 7) \\
  Verbano-Cusio-Ossola &   867.79 &     4.40 &   1.40 &      5.76 &  (2, 1, 0) &  (0, 0, 0, 7) \\
              Vercelli &   877.95 &     2.88 &   1.59 &      0.40 &  (1, 1, 2) &  (0, 0, 0, 7) \\
                Verona &  1083.25 &     3.44 &   1.33 &      3.90 &  (1, 1, 2) &  (2, 0, 0, 7) \\
         Vibo Valentia &   453.04 &     0.12 &   0.33 &      0.95 &  (0, 1, 2) &  (2, 0, 0, 7) \\
               Vicenza &   922.14 &     1.19 &   0.71 &      1.18 &  (0, 1, 1) &  (1, 0, 0, 7) \\
               Viterbo &   689.54 &    45.68 &   1.83 &    104.43 &  (2, 1, 2) &  (0, 0, 0, 7) \\
\bottomrule
\end{tabular}


prov_df_res.to_csv("../results/sarimax_prov.csv", index=False)


prov_df_res.plot(x="Province", y="AIC", kind="bar", figsize=(16,5), legend=False, xlabel="", ylabel="AIC")
plt.show()


prov_df_res.plot(x="Province", y="MAE", kind="bar", figsize=(16,5), legend=False, xlabel="", ylabel="MAE", color="g")
plt.show()


prov_df_res.plot(x="Province", y=["MSE", "CV_MSE"], kind="bar", figsize=(16,5), xlabel="", ylabel="MSE")
plt.show()


prov_df_res.loc[(prov_df_res.MSE < 15)].plot(x="Province", y=["MSE", "CV_MSE"], kind="bar", figsize=(16,5), xlabel="", ylabel="MSE")
plt.show()


prov_df_res.loc[(prov_df_res.MSE > 15) & (prov_df_res.Province != "Trento")].plot(x="Province", y=["MSE", "CV_MSE"], kind="bar", figsize=(16,5), xlabel="", ylabel="MSE")
plt.show()


reg_auto_sarimax = {}
aics, maes, mses, orders, sorders, cv_scores = [], [], [], [], [], []
from tqdm import tqdm
for reg in tqdm(dpc_regioni_df.denominazione_regione.unique()):
    compart = "nuovi_positivi"
    date = 'data'

    tmp_df = dpc_regioni_df[dpc_regioni_df.denominazione_regione == reg].query('20200701 > data')
    tmp_df = tmp_df.set_index(date)

    train = tmp_df[[compart]].query('20200615 > data')
    test = tmp_df[[compart]].query('20200615 <= data')

    smodel = pm.auto_arima(
        train, start_p=1, start_q=1,
        test='adf', m=7, seasonal=True,
        stepwise=True, n_jobs=-1)
    
    cv = model_selection.SlidingWindowForecastCV(window_size=7, step=7, h=7)
    cv_model_scores = model_selection.cross_val_score(smodel, test, scoring='mean_squared_error', cv=cv, verbose=0)

    cv_scores.append(np.average(cv_model_scores))
    
    aics.append(smodel.aic())
    orders.append(smodel.order)
    sorders.append(smodel.seasonal_order)
    
    yhat, ci = smodel.predict(n_periods=len(test), return_conf_int=True)
    maes.append(mean_absolute_error(test, yhat))
    mses.append(mean_squared_error(test, yhat))

reg_auto_sarimax["Region"] = dpc_regioni_df.denominazione_regione.unique()
reg_auto_sarimax["AIC"] = aics
reg_auto_sarimax["MSE"] = mses
reg_auto_sarimax["MAE"] = maes
reg_auto_sarimax["CV_MSE"] = cv_scores
reg_auto_sarimax["Order"] = orders
reg_auto_sarimax["Season_Order"] = sorders

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reg_df_res = pd.DataFrame.from_dict(reg_auto_sarimax)
reg_df_res


reg_df_res.to_csv("../results/sarimax_reg.csv", index=False)


reg_df_res.plot(x="Region", y="AIC", kind="bar", figsize=(8,5), legend=False, xlabel="", ylabel="AIC")
plt.show()


reg_df_res.plot(x="Region", y="MAE", kind="bar", figsize=(8,5), legend=False, xlabel="", ylabel="MAE", color="g")
plt.show()


reg_df_res.loc[(reg_df_res.Region != "Lombardia") & (reg_df_res.Region != "Campania")].plot(x="Region", y="MAE", kind="bar", figsize=(8,5), legend=False, xlabel="", ylabel="MAE", color="g")
plt.show()


reg_df_res.plot(x="Region", y=["MSE", "CV_MSE"], kind="bar", figsize=(8,5), xlabel="", ylabel="MSE")
plt.show()


reg_df_res.loc[(reg_df_res.Region != "Lombardia") & (reg_df_res.Region != "Campania")].plot(x="Region", y=["MSE", "CV_MSE"], kind="bar", figsize=(8,5), xlabel="", ylabel="MSE")
plt.show()


reg_df_res.loc[(reg_df_res.Region != "Lombardia") & (reg_df_res.Region != "Campania") & (reg_df_res.Region != "Emilia-Romagna") & (reg_df_res.Region != "Lazio") & (reg_df_res.Region != "Piemonte")].plot(x="Region", y=["MSE", "CV_MSE"], kind="bar", figsize=(8,5), xlabel="", ylabel="MSE")
plt.show()


tmp_df = covidpro_df[covidpro_df.Province == province].query('20200801 > Date')
tmp_df[compart] = tmp_df[compart].apply(lambda x: 0 if x is np.nan or x < 0 else x)
tmp_df = tmp_df.set_index(date)

tmp_df = tmp_df[[compart]]


data = pd.DataFrame(tmp_df[compart].copy())


data.columns = ["y"]
data["weekday"] = data.index.weekday


for i in range(1, 30):
    data["lag_{}".format(i)] = data.y.shift(i)


from sklearn.linear_model import LinearRegression
from sklearn.model_selection import cross_val_score, TimeSeriesSplit

# for time-series cross-validation set 5 folds 
tscv = TimeSeriesSplit(n_splits=5)


def timeseries_train_test_split(X, y, test_size):
    """
        Perform train-test split with respect to time series structure
    """
    
    # get the index after which test set starts
    test_index = int(len(X)*(1-test_size))
    
    X_train = X.iloc[:test_index]
    y_train = y.iloc[:test_index]
    X_test = X.iloc[test_index:]
    y_test = y.iloc[test_index:]
    
    return X_train, X_test, y_train, y_test


y = data.dropna().y
X = data.dropna().drop(['y'], axis=1)

# reserve 30% of data for testing
X_train, X_test, y_train, y_test = timeseries_train_test_split(X, y, test_size=0.3)


lr = LinearRegression()
lr.fit(X_train, y_train)

LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)


def plotModelResults(model, X_train=X_train, X_test=X_test, plot_intervals=False, plot_anomalies=False):
    """
        Plots modelled vs fact values, prediction intervals and anomalies
    
    """
    
    prediction = model.predict(X_test)
    
    plt.figure(figsize=(15, 7))
    plt.plot(prediction, "g", label="prediction", linewidth=2.0)
    plt.plot(y_test.values, label="actual", linewidth=2.0)
    
    if plot_intervals:
        cv = cross_val_score(model, X_train, y_train, 
                                    cv=tscv, 
                                    scoring="neg_mean_absolute_error")
        mae = cv.mean() * (-1)
        deviation = cv.std()
        
        scale = 1.96
        lower = prediction - (mae + scale * deviation)
        upper = prediction + (mae + scale * deviation)
        
        plt.plot(lower, "r--", label="upper bound / lower bound", alpha=0.5)
        plt.plot(upper, "r--", alpha=0.5)
        
        if plot_anomalies:
            anomalies = np.array([np.NaN]*len(y_test))
            anomalies[y_test<lower] = y_test[y_test<lower]
            anomalies[y_test>upper] = y_test[y_test>upper]
            plt.plot(anomalies, "o", markersize=10, label = "Anomalies")
    
    error = mean_squared_error(prediction, y_test)
    plt.title("Mean squared error {0:.2f}%".format(error))
    plt.legend(loc="best")
    plt.tight_layout()
    plt.show()
    
def plotCoefficients(model):
    """
        Plots sorted coefficient values of the model
    """
    
    coefs = pd.DataFrame(model.coef_, X_train.columns)
    coefs.columns = ["coef"]
    coefs["abs"] = coefs.coef.apply(np.abs)
    coefs = coefs.sort_values(by="abs", ascending=False).drop(["abs"], axis=1)
    
    plt.figure(figsize=(15, 7))
    coefs.coef.plot(kind='bar')
    #plt.grid(True, axis='y')
    #plt.hlines(y=0, xmin=0, xmax=len(coefs), linestyles='dashed')
    plt.hlines(y=0, xmax=len(coefs))
    plt.show()


plotModelResults(lr)
plotCoefficients(lr)


from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()


y = data.dropna().y
X = data.dropna().drop(['y'], axis=1)

X_train, X_test, y_train, y_test = timeseries_train_test_split(X, y, test_size=0.3)

X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

lr = LinearRegression()
lr.fit(X_train_scaled, y_train)

plotModelResults(lr, X_train=X_train_scaled, X_test=X_test_scaled)
plotCoefficients(lr)


from sklearn.linear_model import LassoCV, RidgeCV

ridge = RidgeCV(cv=tscv)
ridge.fit(X_train_scaled, y_train)

plotModelResults(ridge, 
                 X_train=X_train_scaled, 
                 X_test=X_test_scaled, 
                 plot_intervals=True, plot_anomalies=True)
plotCoefficients(ridge)


from xgboost import XGBRegressor 

xgb = XGBRegressor()
xgb.fit(X_train_scaled, y_train)

XGBRegressor(base_score=0.5, booster='gbtree', colsample_bylevel=1,
             colsample_bynode=1, colsample_bytree=1, gamma=0, gpu_id=-1,
             importance_type='gain', interaction_constraints='',
             learning_rate=0.300000012, max_delta_step=0, max_depth=6,
             min_child_weight=1, missing=nan, monotone_constraints='()',
             n_estimators=100, n_jobs=8, num_parallel_tree=1,
             objective='reg:squarederror', random_state=0, reg_alpha=0,
             reg_lambda=1, scale_pos_weight=1, subsample=1, tree_method='exact',
             validate_parameters=1, verbosity=None)


plotModelResults(xgb, 
                 X_train=X_train_scaled, 
                 X_test=X_test_scaled)

	name	param	optimized
smoothing_level	alpha	0.158386	True
smoothing_trend	beta	0.224553	True
initial_level	l.0	-4.269623	True
initial_trend	b.0	-0.186765	True

Dep. Variable:	New_cases	No. Observations:	112
Model:	AutoReg(1)	Log Likelihood	-526.365
Method:	Conditional MLE	S.D. of innovations	27.746
Date:	Mon, 28 Dec 2020	AIC	6.700
Time:	18:36:34	BIC	6.773
Sample:	02-25-2020	HQIC	6.730
	- 06-14-2020

	coef	std err	z	P>\|z\|	[0.025	0.975]
intercept	10.0673	3.423	2.941	0.003	3.359	16.776
New_cases.L1	0.6832	0.069	9.876	0.000	0.548	0.819

	Real	Imaginary	Modulus	Frequency
AR.1	1.4638	+0.0000j	1.4638	0.0000

	0	1
intercept	3.358958	16.775667
New_cases.L1	0.547580	0.818741

Time series¶

Exploration TS: infected Firenze¶

Exploration TS: deaths Firenze¶

Exploration TS: infected Piemonte¶

Anomalies plot¶

Prediction¶

Exponential Smoothing and Holt-Winters¶

Deasonalize, detrend and make stationary¶

AR¶

MA¶

ARMA¶

ARIMA¶

AR¶

Deseasonalized, detrended and stationary¶

MA¶

Deseasonalized, detrended and stationary¶

ARMA¶

Deseasonalized, detrended and stationary¶

ARIMA¶

Deseasonalized, detrended and stationary¶

SARIMAX¶

Auto-SARIMAX¶

Grid-search all provinces¶

Grid-search all regions¶

Time series as Supervised classification¶

	name	param	optimized
smoothing_level	alpha	0.318692	True
initial_level	l.0	1.051003	True

Ljung-Box (L1) (Q):	4.87	Jarque-Bera (JB):	1793.73
Prob(Q):	0.03	Prob(JB):	0.00
Heteroskedasticity (H):	0.50	Skew:	3.31
Prob(H) (two-sided):	0.04	Kurtosis:	21.45

	0	1
const	18.333761	44.070953
ma.L1	0.360067	0.670836
sigma2	854.303397	1096.922155

Ljung-Box (L1) (Q):	0.06	Jarque-Bera (JB):	4387.59
Prob(Q):	0.80	Prob(JB):	0.00
Heteroskedasticity (H):	0.07	Skew:	3.83
Prob(H) (two-sided):	0.00	Kurtosis:	32.69

	0	1
const	-72.364330	116.820508
ar.L1	0.827864	1.489956
ar.L2	-0.479207	0.108793
ma.L1	-1.072090	-0.450736
sigma2	601.193356	718.709456

	0	1
ar.L1	-0.042979	0.430930
ma.L1	-0.947893	-0.608879
sigma2	617.933265	726.680153

	0	1
const	-0.216423	2.672056
ma.L1	-0.159981	0.277204
sigma2	41.709039	54.745247

	0	1
const	-0.140142	2.597186
ar.L1	-2.562510	1.675022
ar.L2	-0.364231	0.222360
ma.L1	-1.694703	2.701597
sigma2	41.133890	54.160118

	0	1
ar.L1	-0.154788	0.271799
ma.L1	-2.154180	0.155689
sigma2	-6.988208	104.446185

	parameters	aic
0	(2, 3, 1, 1)	817.105015
1	(2, 2, 1, 1)	817.170147
2	(2, 4, 1, 1)	818.543111
3	(3, 2, 1, 1)	818.644448
4	(3, 3, 1, 1)	818.823863

	coef	std err	z	P>\|z\|	[0.025	0.975]
const	31.2024	6.566	4.752	0.000	18.334	44.071
ma.L1	0.5155	0.079	6.502	0.000	0.360	0.671
sigma2	975.6128	61.894	15.763	0.000	854.303	1096.922

	coef	std err	z	P>\|z\|	[0.025	0.975]
const	22.2281	48.262	0.461	0.645	-72.364	116.821
ar.L1	1.1589	0.169	6.861	0.000	0.828	1.490
ar.L2	-0.1852	0.150	-1.235	0.217	-0.479	0.109
ma.L1	-0.7614	0.159	-4.804	0.000	-1.072	-0.451
sigma2	659.9514	29.979	22.014	0.000	601.193	718.709

	coef	std err	z	P>\|z\|	[0.025	0.975]
ar.L1	0.1940	0.121	1.604	0.109	-0.043	0.431
ma.L1	-0.7784	0.086	-9.000	0.000	-0.948	-0.609
sigma2	672.3067	27.742	24.234	0.000	617.933	726.680

	coef	std err	z	P>\|z\|	[0.025	0.975]
intercept	0.9854	0.599	1.646	0.100	-0.188	2.159
y.L1	0.0469	0.089	0.526	0.599	-0.128	0.222

	0	1
ar.L1	-1.711645	-1.336380
ar.L2	-1.059836	-0.757594
ma.L1	-13.921534	15.160256
ma.L2	-24.346197	23.082654
ma.L3	-15.566891	13.592808
ar.S.L7	-0.411464	-0.090980
ma.S.L7	-0.829505	-0.518677
sigma2	-604.528511	692.848032

Ljung-Box (L1) (Q):	0.01	Jarque-Bera (JB):	128.44
Prob(Q):	0.93	Prob(JB):	0.00
Heteroskedasticity (H):	0.06	Skew:	-0.61
Prob(H) (two-sided):	0.00	Kurtosis:	8.13

	Province	AIC	MSE	MAE	CV_MSE	Order	Season_Order
0	Agrigento	503.72	0.00	0.00	0.00	(2, 1, 1)	(0, 0, 0, 7)
1	Alessandria	1101.68	68.62	7.24	148.68	(0, 1, 1)	(0, 0, 0, 7)
2	Ancona	853.51	0.79	0.87	0.16	(1, 1, 2)	(2, 0, 0, 7)
3	Aosta	889.98	0.33	0.33	0.37	(1, 1, 1)	(0, 0, 1, 7)
4	Arezzo	807.62	2.51	1.12	1.83	(1, 1, 2)	(0, 0, 0, 7)
...	...	...	...	...	...	...	...
86	Vercelli	877.95	2.88	1.59	0.40	(1, 1, 2)	(0, 0, 0, 7)
87	Verona	1083.25	3.44	1.33	3.90	(1, 1, 2)	(2, 0, 0, 7)
88	Vibo Valentia	453.04	0.12	0.33	0.95	(0, 1, 2)	(2, 0, 0, 7)
89	Vicenza	922.14	1.19	0.71	1.18	(0, 1, 1)	(1, 0, 0, 7)
90	Viterbo	689.54	45.68	1.83	104.43	(2, 1, 2)	(0, 0, 0, 7)

	Region	AIC	MSE	MAE	CV_MSE	Order	Season_Order
0	Abruzzo	1006.348650	6.161070	2.399735	1.327821	(0, 1, 1)	(0, 0, 0, 7)
1	Basilicata	644.910513	0.066212	0.192989	0.000000	(1, 1, 2)	(0, 0, 0, 7)
2	Calabria	862.912192	3.228955	1.158507	16.034059	(0, 1, 1)	(0, 0, 1, 7)
3	Campania	1105.382576	1474.858602	37.782933	66.777285	(0, 1, 1)	(0, 0, 0, 7)
4	Emilia-Romagna	1258.708031	198.283326	10.553271	261.641842	(0, 1, 1)	(2, 0, 0, 7)
5	Friuli Venezia Giulia	991.315467	2.920540	1.459127	0.983586	(0, 1, 1)	(1, 0, 0, 7)
6	Lazio	952.412988	73.433064	7.821605	31.283066	(1, 1, 0)	(0, 0, 1, 7)
7	Liguria	1119.749044	11.070229	2.348895	16.560588	(1, 1, 3)	(0, 0, 0, 7)
8	Lombardia	1580.473527	16276.255836	115.781523	8800.647219	(0, 1, 1)	(1, 0, 0, 7)
9	Marche	1038.394727	4.258527	1.822247	4.583801	(1, 1, 2)	(0, 0, 1, 7)
10	Molise	707.235321	0.645035	0.468081	1.183678	(0, 1, 1)	(0, 0, 0, 7)
11	Piemonte	1359.711046	340.576072	16.170122	168.109789	(0, 1, 1)	(1, 0, 0, 7)
12	Puglia	999.438448	19.686953	3.354832	45.143754	(0, 1, 2)	(1, 0, 1, 7)
13	Sardegna	894.163790	0.647699	0.677119	0.326518	(0, 1, 1)	(0, 0, 0, 7)
14	Sicilia	891.195368	0.921696	0.805941	2.035445	(2, 1, 2)	(0, 0, 0, 7)
15	Toscana	1155.799097	18.512890	3.961160	12.102047	(0, 1, 1)	(0, 0, 0, 7)
16	Trentino Alto Adige	1104.526479	13.369835	3.049131	12.479118	(0, 1, 1)	(1, 0, 0, 7)
17	Umbria	790.411483	0.340768	0.413676	0.371690	(1, 1, 2)	(0, 0, 1, 7)
18	Valle d'Aosta	890.690159	0.333739	0.329483	0.366910	(1, 1, 1)	(0, 0, 1, 7)
19	Veneto	1260.332229	33.382835	4.304954	12.708689	(1, 1, 0)	(1, 0, 1, 7)